Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations

Authors:
J. A. Atwell;B. B. King
Affiliations:
Center for Optimal Design and Control Interdisciplinary Center for Applied Mathematics Virginia Tech, Blacksburg, VA 24061-0531, U.S.A.;Center for Optimal Design and Control Interdisciplinary Center for Applied Mathematics Virginia Tech, Blacksburg, VA 24061-0531, U.S.A.
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2001

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Abstract

In this paper, we present a discussion of the proper orthogonal decomposition (POD) as applied to simulation and feedback control of the one-dimensional heat equation. We provide two examples of input collections to which the POD process is applied. First, we apply POD directly to the finite element basis of linear B-splines. Next, we additionally include time snapshots. We show that although the second case provides better simulations, this POD basis is ill-suited for control problems. We provide a discussion of both the linear quadratic regulator (LQR) problem and the linear quadratic Gaussian (LQG) problem.